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Question 1 of 4
Find the determinant of the matrix:
[42-13]
Incorrect
A determinant is a real number associated with a square matrix.
Determinant of a 2×2 Matrix
If [abcd] then |A|=ad−bc
First, label the values of the matrix
Substitute the values into the Determinant Formula
|abcd| |
= |
ad -bc |
Determinant Formula |
|
|42−13| |
= |
4⋅3 -2⋅(-1) |
Determinant Formula |
|
|
= |
12-(-2) |
|
= |
14 |
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Question 2 of 4
Find the determinant of the matrix:
[6-23-5]
Incorrect
A determinant is a real number associated with a square matrix.
Determinant of a 2×2 Matrix
If [abcd] then |A|=ad−bc
First, label the values of the matrix
Substitute the values into the Determinant Formula
|abcd| |
= |
ad -bc |
Determinant Formula |
|
|6−23−5| |
= |
6⋅(-5) --2⋅3 |
Determinant Formula |
|
|
= |
-30-(-6) |
|
= |
-24 |
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Question 3 of 4
Find the determinant of the matrix:
[30-47]
Incorrect
A determinant is a real number associated with a square matrix.
Determinant of a 2×2 Matrix
If [abcd] then |A|=ad−bc
First, label the values of the matrix
Substitute the values into the Determinant Formula
|abcd| |
= |
ad -bc |
Determinant Formula |
|
|30−47| |
= |
3⋅7 -0⋅(-4) |
Determinant Formula |
|
|
= |
21-0 |
|
= |
21 |
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Question 4 of 4
Find the determinant of the matrix:
A=[411-2011-12]
Incorrect
A determinant is a real number associated with a square matrix.
Determinant of a 3×3 Matrix
If A=[abcdefghk] then |A|=a|efhk|−b|dfgk|+c|degh|
Determinant of a 2×2 Matrix
If [abcd] then |A|=ad−bc
First, label the values of the matrix
[abcdefghk]=[411−2011−12]
Substitute the values into the Determinant Formula and solve each term
|A| |
= |
|abcdefghk| |
= |
a|efhk|−b|dfgk|+c|degh| |
Determinant of a 3×3 Matrix |
|
|
|
|411−2011−12| |
= |
4|01−12|−1|−2112|+1|−201−1| |
Substitute values |
|
= |
[4(0⋅2−1⋅(−1))]−[1(−2⋅2−1⋅1)]+[1(−2⋅(−1)−0⋅1)] |
|
= |
4(0-(-1))-1(-4-1)+1(2-0) |
|
= |
4(1)-1(-5)+1(2) |
|
= |
4+5+2 |
|A| |
= |
11 |